Advanced Mathematical Modeling in Engineering

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• MASAHİRO YAMAMOTO

In this review, concerning parabolic equations, we give self-contained descriptions on (1) derivations of Carleman estimates;(2) methods for applications of the Carleman estimates to estimates of solutions and to inverse problems.Moreover limited to parabolic equations, we survey the previous and recent results in vie…

• MASAHİRO YAMAMOTO

Abstract In this paper, a multi‐scale analysis method for heat transfer in heterogeneous solids is presented. The principles of the method rely on a two‐scale computational homogenization approach which is applied successfully for the stress analysis of multi‐phase solids under purely mechanical loading. The present p…

• İZZET ÖZDEMİR

We consider a system with a suitable boundary condition, where is a bounded domain, is a uniformly elliptic operator of the second order whose coefficients are suitably regular for , is fixed, and a function satisfies Our inverse problems are determinations of g using overdetermining data or , where and . Our main res…

For the solution u ( p ) = u ( p )( x , t ) to ∂ t 2 u ( x , t )-Δ u ( x , t )- p ( x ) u ( x , t ) = 0 in Ω × (0, T ) and (∂ u /∂ν)| ∂Ω × (0, T ) = 0 with given u (·,0) and ∂ t u (·,0), we consider an inverse problem of determining p ( x ), x ∊Ω, from data u |ω × (0, T ) . Here Ω⊂ n , n = 1,2,3, is a bounded domain,…

This paper presents a variational multiscale method (VMS) for the incompressible Navier--Stokes equations which is defined by a large scale space L H for the velocity deformation tensor and a turbulent viscosity $\nu_T$. The connection of this method to the standard formulation of a VMS is explained. The conditions on…

• SONGÜL KAYA MERDAN

We consider an inverse problem of determining p(x), x ∈ Ω in (∂2 u/∂t 2)(x, t) − Δu(x, t) − p(x)u(x, t) = 0 in Ω × (0, T) and (∂u/∂ν)|∂Ω×(0, T) = 0 with given u(·, 0) and (∂u/∂t)(·, 0). Here Ω ⊂ R n , n = 1, 2, 3, is a bounded domain. We prove the Lipschitz stability in determining p from u|∂Ω×(0,T), under the assumpt…

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Let u(f) be the solution to a hyperbolic equation in a bounded domain Omega subset R ': u"(x, t) = Delta u(x,t) + sigma (t)f(x) (x in Omega, 0 < t < T) u(x,0) = 0 u'(x,0) = 0 (x in Omega) u(x,t) = 0 (x in partial Omega, 0 < t < T). We assume that sigma in C 1 [0,T] is a known function, sigma(0) not= 0, and f in L 2 (O…

We study the stability of a flexible beam that is clamped at one end and free at the other; a mass is also attached to the free end of the beam. To stabilize this system we apply a boundary control force at the free end of the beam. We prove that the closed-loop system is well-posed and is exponentially stable. We the…

We prove for a two-dimensional bounded domain that the Cauchy data for the Schrödinger equation measured on an arbitrary open subset of the boundary uniquely determines the potential. This implies, for the conductivity equation, that if we measure the current fluxes at the boundary on an arbitrary open subset of the b…

• MASAHİRO YAMAMOTO

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